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Closed graph and open mapping theorems for topological -modules and applications

✍ Scribed by Claudia Garetto

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
369 KB
Volume
282
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

We present closed graph and open mapping theorems for $ \tilde \lc $‐linear maps acting between suitable classes of topological and locally convex topological $ \tilde \lc $‐modules. This is done by adaptation of De Wilde's theory of webbed spaces and Adasch–Ernst–Keim's theory of barrelled spaces to the context of locally convex and topological $ \tilde \lc $‐modules, respectively. We give applications of the previous theorems to Colombeau theory as well to the theory of Banach $ \tilde \lc $‐modules. In particular we obtain a necessary condition for 𝒢^∞^‐hypoellipticity on the symbol of a partial differential operator with generalized constant coefficients (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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